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Question #43454

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The Question

A full-wave rectifier circuit provides a peak output voltage of $V_0 = 100 \text{ V}$ . It is connected to a filter capacitor $C = 1000 \text{ } \mu\text{F}$ in parallel with a DC motor. The motor has an armature resistance $R = 10 \text{ } \Omega$ and negligible inductance. At $t = 0$ , the rectifier diodes become reverse-biased exactly as the capacitor voltage reaches its peak $V_0$ . At this instant, the motor is running with a back-EMF $E = 50 \text{ V}$ , which is increasing at a constant rate of $500 \text{ V/s}$ due to the motor's acceleration. Assuming ideal components, what is the instantaneous rate of change of the current flowing through the motor, $\frac{dI}{dt}$ , at $t = 0^+$ ?

Options

A.
$-550 \text{ A/s}$
B.
$-500 \text{ A/s}$
C.
$-450 \text{ A/s}$
D.
$-1050 \text{ A/s}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Rectifier Ripple Factor|Kirchhoff’s Junction Rule|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to apply Kirchhoff's laws to a transient circuit where the load is not a static resistance, but a dynamic element (a motor with a time-varying back-EMF).

A common trap is to rely on standard static ripple approximations or to ignore the $\frac{dE}{dt}$ term when differentiating the voltage loop equation.

Students often incorrectly assume that the rate of change of current depends solely on the capacitor's discharge rate ( $\frac{dV_C}{dt}$ ), failing to recognize that the time-varying back-EMF acts as an opposing dynamic voltage source that accelerates the decay of the load current.

Other traps include ignoring the back-EMF entirely when calculating the initial current, or making a sign error when accounting for the opposing nature of the back-EMF derivative.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Semiconductor Electronics: Materials, Devices, and Simple Circuits - Class 12
Concept	Rectifier Ripple Factor
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free